Rankine Cycle Reading Problems 11.1 ! 11.7 11.29, 11.36, 11.43, 11.47, 11.52, 11.55, 11.58, 11.74 Definitions • working fluid is alternately vaporized and condensed as it recirculates in a closed cycle • the standard vapour cycle that excludes internal irreversibilities is called the Ideal Rankine Cycle Analyze the Process Device 1st Law Balance Boiler h2 + qH = h3 ) qH = h3 − h2 (in) Turbine h3 = h4 + wT ) wT = h3 − h4 (out) Condenser h4 = h1 + qL ) qL = h4 − h1 (out) Pump h1 + wP = h2 ) wP = h2 − h1 (in) 1 The Rankine efficiency is net work output ηR = heat supplied to the boiler (h − h ) + (h − h ) = 3 4 1 2 (h3 − h2) Effects of Boiler and Condenser Pressure We know the efficiency is proportional to T η / 1 − L TH The question is ! how do we increase efficiency ) TL # and/or TH ". 1. INCREASED BOILER PRESSURE: • an increase in boiler pressure results in a higher TH for the same TL, therefore η ". • but 40 has a lower quality than 4 – wetter steam at the turbine exhaust – results in cavitation of the turbine blades – η # plus " maintenance • quality should be > 80 − 90% at the turbine exhaust 2 2. LOWER TL: • we are generally limited by the T ER (lake, river, etc.) eg. lake @ 15 ◦C + ∆T = 10 ◦C = 25 ◦C | {z } resistance to HT ) Psat = 3:169 kP a. • this is why we have a condenser – the pressure at the exit of the turbine can be less than atmospheric pressure 3. INCREASED TH BY ADDING SUPERHEAT: • the average temperature at which heat is supplied in the boiler can be increased by superheating the steam – dry saturated steam from the boiler is passed through a second bank of smaller bore tubes within the boiler until the steam reaches the required temperature – The value of T H , the mean temperature at which heat is added, increases, while TL remains constant. Therefore the efficiency increases. 3 Rankine Cycle with Reheat • the wetness at the exhaust of the turbine should be no greater that 10% - this can result in physical erosion of the turbine blades • but high boiler pressures are required for high efficiency - tends to lead to a high wetness ratio • to improve the exhaust steam conditions, the steam can be reheated with the expansion car- ried out in two steps HighPressure LowPressure T Turbine Turbine QRH Steam Generator WT QH QRH QH QL Condenser Pump s WP Rankine Cycle with Regeneration • Carnot cycle has efficiency: η = 1 − TL=TH – add QH at as high a TH as possible – reject QL at as low a TL as possible • the Rankine cycle can be used with a Feedwater Heater to heat the high pressure sub-cooled water at the pump exit to the saturation temperature – most of the heat addition (QH ) is done at high temperature 4 Feedwater Heaters There are two different types of feedwater heaters 1. OPEN FWH: the streams mix ! high temperature steam with low temperature water at constant pressure 2. CLOSED FWH: a heat exchanger is used to transfer heat between the two streams but the streams do not mix. The two streams can be maintained at different pressures. OPEN FWH: • working fluid passes isentropically through the turbine stages and pumps • steam enters the first stage turbine at state 5 and expands to state 6 - where a fraction of the total flow is bled off into an open feedwater heater • the rest of the steam expands into the second stage turbine at state point 7 - this portion of the fluid is condensed and pumped as a saturated liquid to the FWH at state 2 • a single mixed stream exists the FWH at state point 3 5 6 CLOSED FWH: two variations exist Case 1: pump the condensate back to the high pressure line • a steam trap is inserted in the condensed steam line that allows only liquid to pass • liquid is passed to a low pressure region such as the condenser or a low pressure heater Case 2: the incoming feedwater does not mix with the extracted steam • both streams flow separately through the heater • the two streams can have different pressures 7 8 Binary Cycle • involves two Rankine cycles running in tandem with different working fluids such as mercury and water • why: – typically a boiler will supply energy at 1300 − 1400 ◦C ◦ – but Tcritical for water is 374:14 C ∗ most energy is absorbed below this temperature ∗ high ∆T between the boiler source and the water leads to a major source of irre- versibilities ◦ – Tcritical for mercury is about 1500 C ∗ no need for superheating 9 10 PROBLEM STATEMENT: Water is the working fluid for a Rankine cycle process where the turbine and the pump have isentropic efficiencies of 85% and 70%, respectively. Superheated vapor enters the turbine at 8 MP a and 500 ◦C. The condenser pressure is 7:5 kP a. The net power output of the cycle is 100 MW . Determine for the cycle: a) the mass flow rate of the steam [kg=s], for a net power output of 100 MW . b) the rate of heat transfer [MW ] to the working fluid passing through the steam generator. c) the thermal efficiency. d) the mass flow rate of the condenser cooling water [kg=h], if the cooling water enters the condenser at 15 ◦C and exits at 35 ◦C, with negligible pressure change. 11.